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Paper Citation Record · LEDGER

Coefficients of $q$-real numbers: their combinatorial meaning and growth

As of 12 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2608.06761.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.06761 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:21:12.201646Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

  • verified exact5
  • verified fuzzy13
  • unresolved12
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 80a60f50-5e51-4a5c-9dbd-b9db2cc177d9 · outbound

This paper cites Aval and S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Aval and S

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.062871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation af949a37-6a14-4068-841f-a6b792b8931f · outbound

This paper cites Bapat, L.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Bapat, L

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.067937Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.067937Z digest=sha256:69b5be9d687cc01bf5653ca84ef3f000483738dc1f8aa72bd71c3ce2bc8513f0

Observation 09497fca-ba66-49b8-a6fe-b5f303697301 · outbound

This paper cites Cayley,On the theory of the analytical forms called trees, Phil.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Cayley,On the theory of the analytical forms called trees, Phil

Reference 3

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 4eb9bcd6-6ba7-4faa-8b95-1507c67eed8f · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 4

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.076967Z digest=sha256:073a874c4dc243487d1c7e44b7c3273dd84f6364e30b14ffff2d8ed859bc39fc

Observation a825f172-03c6-4bdf-9f7b-cb1a731da7fa · outbound

This paper cites Deutsch and L.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Deutsch and L

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.898861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 9f8e9511-6a23-4e67-b088-40275b4d91f6 · outbound

This paper cites Bounding deformation spaces of Kleinian groups with two generators.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Bounding deformation spaces of Kleinian groups with two generators

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.086904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.086904Z digest=sha256:3bf0abfcc13b700cc6567b70d92fd2945f9e53213c5fae61a8d406b22e64b20d

Observation e30f70d4-3e9f-4431-b3d1-d9a20c62a0dd · outbound

This paper cites On $q$-real and $q$-complex numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth On $q$-real and $q$-complex numbers

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.091519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.091519Z digest=sha256:b96bd6e0f446991a158782167c19259c6bc208f1e6a123e7e31840711aa5a4d7

Observation bccd78ad-9ab8-48c4-8cfb-b8da6dabb1b9 · outbound

This paper cites Evans, A.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Evans, A

Reference 8

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.276208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.096135Z digest=sha256:716cf03ed661ee125e94533955b95b12c0429d4952db6012eff096e7836cf9e6

Observation 444ee2bb-d311-4aa1-b4bc-09e48123e9de · outbound

This paper cites Flajolet, R.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Flajolet, R

Reference 9

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.100680Z digest=sha256:ee704476041d0b441d44dbed3debbd5aff5c067e5a3a64fb7d90014cf9a4c567

Observation 2eb740a4-b249-4043-89ee-d2a0448bb7ec · outbound

This paper cites Euler,De evolutione potestatis polynomialis cuiuscunque(1 + x + x2 + x3 + x4 + etc.)n, Nova Acta Academiae Scientiarum Imperialis Petropolitanae,12(1801), 47–57.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Euler,De evolutione potestatis polynomialis cuiuscunque(1 + x + x2 + x3 + x4 + etc.)n, Nova Acta Academiae Scientiarum Imperialis Petropolitanae,12(1801), 47–57

Reference 10

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verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.871287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 1d563068-c1f7-45dd-a3c1-f4a7fc4f9560 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.858963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 92d76c31-152a-4489-9fb3-e35265f4b3c3 · outbound

This paper cites Han and E.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Han and E

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.113761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.113761Z digest=sha256:b1c76c82788348463002b736defa10d5ba0bdab6a538e50ff550f6a7ee2ecffa

Observation 9224c04b-0176-4c92-96b1-b8987fc1dd8f · outbound

This paper cites Hirzebruch,Hilbert modular surfaces, Enseign.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Hirzebruch,Hilbert modular surfaces, Enseign

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.846984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation b0d5c96b-e991-429c-9a48-5cc06fa11fe6 · outbound

This paper cites Leclere and S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Leclere and S

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 6e069ddf-33d6-4d7f-ae76-950c981553f0 · outbound

This paper cites Leclere, S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Leclere, S

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.823680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 23fb2bba-9843-4eac-af64-398505e89e42 · outbound

This paper cites McConville, J.

Coefficients of $q$-real numbers: their combinatorial meaning and growth McConville, J

Reference 16

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.133904Z digest=sha256:d0cbfb9f7dec789d6be866a58b134e4285de88dea0d8243f54bdf7d2a6c28c02

Observation eaf622d3-7f2b-4638-975f-540ae07696fb · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.796077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.138394Z digest=sha256:0c6ef1b176df20e90a7f068bda9dcc09b9bcee6f46a7e8f21b4f81fb8ac0e2bd

Observation a75d7b90-f34e-4a77-bf1d-77f86cd1b249 · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 18

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 0697f705-30a8-4517-bd35-16ea72682c71 · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.147574Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.147574Z digest=sha256:08ef4fef6c758b49b67dead52252459fe6d599cce32739269329b3d8082e4f3a

Observation 9af810ad-8a48-4a15-ae0b-0b1ed1e82b07 · outbound

This paper cites $q$-deformed rationals and irrationals.

Coefficients of $q$-real numbers: their combinatorial meaning and growth $q$-deformed rationals and irrationals

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.152584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.152584Z digest=sha256:ad5bfb0233b1878ccb62b0990a03d342d08602df418de9115242485ca1d3d187

Observation a56c4c9d-5078-4a27-bb2a-a5bf3068bebe · outbound

This paper cites Morier-Genoud, V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud, V

Reference 21

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation c857fcbb-a0b9-4aa6-9eda-959525feffb6 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.745534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 22065148-967e-4657-bf80-046fa64f81de · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.734693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.171130Z digest=sha256:fd6f4a55350c596bbd58eba3934d158ca9dcfde475228af98efc91c689c6e4a7

Observation 064cacbe-ebd7-4fbc-83d8-22341a4d60f3 · outbound

This paper cites Ovenhouse,q-rationals and Finite Schubert Varieties, C.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ovenhouse,q-rationals and Finite Schubert Varieties, C

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.722852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.175812Z digest=sha256:77e5a47929198f8994db50d19b700243df88553d9ef7ac6905bc6b60825a1f5d

Observation ba124cd9-dd66-46d3-806d-a8b59b253916 · outbound

This paper cites Ovsienko and E.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ovsienko and E

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.709319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.180352Z digest=sha256:0e10a8dd8505077e9d83e90dfdb19badcbee57b8609386d26c5f20a635e1ff46

Observation 41dc409e-b4d3-43ff-b2a5-98e1dd491d12 · outbound

This paper cites Analytical properties of $q$-metallic numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Analytical properties of $q$-metallic numbers

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:21:12.328454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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Observation 51297070-7da8-4262-9fa0-8ed58a63d837 · outbound

This paper cites Dimers, filters, and $q$-deformed real numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Dimers, filters, and $q$-deformed real numbers

Reference 27

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:21:12.310137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.188443Z digest=sha256:d33d9cd48d3c683fa8bbc3cceccdaf7586be77cc63e7a0d8b250358c3825700d

Observation a5a125e9-f9bb-4ebc-825e-9c60928387f0 · outbound

This paper cites Ren,On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ren,On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res

Reference 28

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.261192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.193125Z digest=sha256:1bcef03ae6a14e777f5be1145b624c1018e8986d98a723622f3155fc38aa6841

Observation 6bc4f5d0-6254-472f-944b-e91d28720fcd · outbound

This paper cites Ren,Corrigendum to: On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ren,Corrigendum to: On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res

Reference 29

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.243196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.197364Z digest=sha256:b00c9a60fa23b83414873a5ff2ac11c41fa3ba029feb6424f13798ca97e87f59

Observation aabb6e74-79f5-4fb6-8631-1ed5a8926698 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.698008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T21:21:12.201646Z digest=sha256:881355282fb054e60c2d43ba60483ba141aee49e089d5c6ba9725713e282cfff

Pith citing papers

No inbound Pith citation observations are available.